|
|
A164163
|
|
Number of binary strings of length n with equal numbers of 0001 and 1010 substrings.
|
|
1
|
|
|
1, 2, 4, 8, 14, 24, 41, 72, 129, 234, 431, 804, 1512, 2864, 5459, 10452, 20086, 38728, 74871, 145068, 281646, 547764, 1066943, 2081060, 4064097, 7945534, 15549613, 30459088, 59714564, 117160356, 230034585, 451954208, 888513601, 1747769154
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
MAPLE
|
b:= proc(n, t) option remember; `if`(n=0, 1, expand(
b(n-1, [2, 3, 4$2, 6, 3, 6][t])*`if`(t=7, 1/x, 1)+
b(n-1, `if`(t=6, 7, 5))*`if`(t=4, x, 1)))
end:
a:= n-> coeff(b(n, 1), x, 0):
# second Maple program:
a:= proc(n) option remember; `if`(n<6, [1, 2, 4, 8, 14, 24][n+1],
((166*n^3-719*n^2-4319*n+6834) *a(n-1)
+(162*n^3-4025*n^2+23078*n-21720) *a(n-2)
+(58*n^3+459*n^2-10135*n+32226) *a(n-3)
-6*(n-6)*(10*n^2+611*n-4579) *a(n-4)
-4*(n-7)*(218*n^2-3243*n+10692) *a(n-5)
+8*(n-7)*(n-8)*(82*n-339) *a(n-6))/
(n*(110*n^2-1067*n+1938)))
end:
|
|
MATHEMATICA
|
a[n_] := a[n] = If[n < 6, {1, 2, 4, 8, 14, 24}[[n + 1]], (1/(n*(110*n^2 - 1067*n + 1938)))*(-(4*(n - 7)*(218*n^2 - 3243*n + 10692)*a[n - 5]) - 6*(n - 6)*(10*n^2 + 611*n - 4579)*a[n - 4] + (58*n^3 + 459*n^2 - 10135*n + 32226)*a[n - 3] + (162*n^3 - 4025*n^2 + 23078*n - 21720)*a[n - 2] + (166*n^3 - 719*n^2 - 4319*n + 6834)*a[n - 1] + 8*(82*n - 339)*(n - 8)*(n - 7)*a[n - 6])];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|